Probabilities are a branch of mathematics that is dedicated to the study of certain so-called randomized experiments, ie coming from the random, which we know all the possible outcomes, but can’t be sure of what will be theexact outcome of the experiment.
Description.
The probability is measured by a number between 0 and 1, if an event never occurs its probability is 0, while if the event occurs its probability is 1. Thus, the odds usually come expressed as fractions or percentages.
Classification
Classical Probability: This type of probability takes an objective and may be viewed in two ways: a priori and a posteriori.
Prior probabilities: The probability of an event A, P (A), is the measure of the chance when this event occurs.
P(A)= # of ways A can occur / # total possible outcomes.
P(A) = A (events corresponding to A) / S (total events in the sample space).
° Posterior probability: In the case that events do not have equal chance of occurrence, the problem of assigning probabilities happens to posterior.
If an experiment is performed a large number of repeated times, N times for example, let n will be the number of times that happens an event E. Then observed that asN increases the n / N tends to a stable value p. This value p is called the probability of E and we write p (E).
Subjective Probability: It refers to the probability of occurrence of an event based on previous experiences, personal opinion, knowledge or intuition of an individual. In this case, after studying the information available, it is assigned a value of probability to events based on our degree of belief that the event might occur.
Frequentist probability:Repeating an experiment under the same conditions many times and repeat until the relative frequency of an event tends to stabilize when the total frequency increases. It applies to randomized experiments that can be repeated under the same conditions the number of times desired.
Comparison & Contrast
Both, the classical and the frequentist definition are based on random repetition of an experiment, but there are many experiments that can not be repeated under the same conditions and, therefore, can not apply the objective interpretation of probability. In such cases, it is necessary to see an alternative view, which isn’t dependson repetition, so when applying subjective probability that is different of the other two, it's possible to make a personal opinion in which different observers may have differentdegrees of belief about possible outcomes, equally valid.
Probability
Definition.
Probabilities are a branch of mathematics that is dedicated to the study of certain so-called randomized experiments, ie coming from the random, which we know all the possible outcomes, but can’t be sure of what will be the exact outcome of the experiment.
Description.
The probability is measured by a number between 0 and 1, if an event never occurs its probability is 0, while if the event occurs its probability is 1. Thus, the odds usually come expressed as fractions or percentages.
Classification
Classical Probability: This type of probability takes an objective and may be viewed in two ways: a priori and a posteriori.
Prior probabilities: The probability of an event A, P (A), is the measure of the chance when this event occurs.
P(A)= # of ways A can occur / # total possible outcomes.
P(A) = A (events corresponding to A) / S (total events in the sample space).
° Posterior probability: In the case that events do not have equal chance of occurrence, the problem of assigning probabilities happens to posterior.
If an experiment is performed a large number of repeated times, N times for example, let n will be the number of times that happens an event E. Then observed that as N increases the n / N tends to a stable value p. This value p is called the probability of E and we write p (E).
Subjective Probability: It refers to the probability of occurrence of an event based on previous experiences, personal opinion, knowledge or intuition of an individual. In this case, after studying the information available, it is assigned a value of probability to events based on our degree of belief that the event might occur.
Frequentist probability: Repeating an experiment under the same conditions many times and repeat until the relative frequency of an event tends to stabilize when the total frequency increases. It applies to randomized experiments that can be repeated under the same conditions the number of times desired.
Comparison & Contrast
Both, the classical and the frequentist definition are based on random repetition of an experiment, but there are many experiments that can not be repeated under the same conditions and, therefore, can not apply the objective interpretation of probability. In such cases, it is necessary to see an alternative view, which isn’t depends on repetition, so when applying subjective probability that is different of the other two, it's possible to make a personal opinion in which different observers may have different degrees of belief about possible outcomes, equally valid.